Chi-Square and Exact Tests for Non-Parametric Functional Dependencies

Statistical hypothesis testing methods for non-parametric functional dependencies using asymptotic chi-square or exact distributions. Functional chi-squares are asymmetric and functionally optimal, unique from other related statistics. Tests in this package reveal evidence for causality based on the causality-by-functionality principle. They include asymptotic functional chi-square tests, an exact functional test, a comparative functional chi-square test, and also a comparative chi-square test. The normalized non-constant functional chi-square test was used by Best Performer NMSUSongLab in HPN-DREAM (DREAM8) Breast Cancer Network Inference Challenges. For continuous data, these tests offer an advantage over regression analysis when a parametric functional form cannot be assumed; for categorical data, they provide a novel means to assess directional dependencies not possible with symmetrical Pearson's chi-square or Fisher's exact tests.



Version 2.3.3 Changes 2016-09-02

  1. Updated the vignettes

Version 2.3.2 Changes 2016-08-29

  1. Updated the reference section to fix the year of Pearson's chi-square test paper which was published in 1900 not 1990.


  1. Now check all options for the method argument so that only valid methods are allowed.

Version 2.3.1 Changes 2016-05-01

  1. Expanded test.interactions() to test many-to-one combinatorial interactions in C++ via Rcpp.

Version 2.3.0 (not deposited to CRAN) Changes 2016-04-30

  1. Data frame input is now converted to numeric matrix before exact functional test.
  2. Added function test.interactions() to test pairwise (one-to-one) interactions, implemented in C++ via Rcpp for computational efficiency.

Version 2.2.4 Changes 2016-04-21

  1. Added vignette "Which statistic to use for functional dependency from fun.chisq.test()?"
  2. Updated references and description.

Version 2.2.3 Changes 2016-03-31

  1. Use [[Rcpp::export]] to automatically generate R interface.


  1. Revised the code to remove dependency on RcppClassic.


  1. Revised help documentation and included new references.

Version 2.2.2 Changes 2016-02-07

  1. Handled a special case for the normalized FunChisq when the degrees of freedom are zero.


  1. Renamed the "type" argument to "alternative" in fun.chisq.test().
  2. Revised values of the "method" argument in fun.chisq.test(). Previous values ("default" and "normalized") are still supported but obsolete.
  3. Added the "log.p" argument in both and cp.chisq.test().
  4. Updated the documentation.


  1. Added a new argument "index.kind" to fun.chisq.test() to specify the function index kind: "unconditional" or "conditional" on a given marginal of Y.


  1. Fixed a bug in cp.chisq.test().

Version 2.2.1 Changes 2016-01-25

  1. Fixed a bug introduced in the previous version.
  2. Updated package description to be more reflective of recent additions.
  3. Included missing references.

Version 2.2.0 Changes 2016-01-23

  1. Improved code efficiency for fun.chisq.test().
  2. Now fun.chisq.test() returns an estimate of function index between 0 and 1, in analogy to Cramer's V, but asymmetrical.
  3. Added additional test examples for fun.chisq.test().


  1. Added type argument to fun.chisq.test() to specify functional or non-constant functional chi-squares.
  2. Added log.p argument to fun.chisq.test() to obtain log of p-value to improve accuracy when sample size is large and p-value is close to zero.

2015-07-03 (Unpublished version 2.1.1 )

  1. Added cp.chisq.test() for comparative chi-square test, not considering functional dependencies.
  2. Added test examples for cp.chisq.test().

Version 2.1.0 2015-06-29 Changes

  1. Substantially reduced the run time of exact functional test by designing a better branch and bound strategy.
  2. Enabled C++11 compling by adding two files (Makevars and
  3. Fixed a bug occured under WIN32 using long double by adding define.h to specify double precision for WIN32 and long double precision for WIN64.
  4. Increased float comparison precision by considering a tolerance.
  5. Imported pnorm() and pchisq() from the "stats" package.

Version 2.0.2 2015-03-03 Changes

  1. Updated documentation for the package and its functions.
  2. Fixed a testing issue under r-release-linux-ix86 flavor.

Version 2.0.1 2015-02-23 Changes

  1. Removed assert() function from StatDistribution.cpp.
  2. Removed Makevar and files.
  3. Removed all iostream and sstream and cassert.
  4. Removed TransitionTableIO.cpp.
  5. In the testthat examples, signif(x,8) is used to compare 8 significant digits of the results.
  6. Added a normalized functional chi-square test example.

Version 2.0.0 2015-02-12 Changes

  1. Added a new exact functional test as a method option to fun.chisq.test(). The exact functional test is an exact version of FunChisq test, it is more precise to detect functional dependencies in small sample-sized contingency tables.
  2. Added a new comparative functional chi-square test for detecting heterogeneity in functional dependencies among contingency tables.
  3. Revised the examples and documentation to improve usability.
  4. Added automated test cases into the package.
  5. Started the NEWS file.

Version 1.0 2014-03-08 Changes

  1. The first release of this package implements the functional chi-square test and a normalized version.

Reference manual

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2.4.3 by Joe Song, 24 days ago

Browse source code at

Authors: Yang Zhang [aut], Hua Zhong [aut], Ruby Sharma [aut], Sajal Kumar [aut], Joe Song [aut, cre]

Documentation:   PDF Manual  

LGPL (>= 3) license

Imports Rcpp, stats

Suggests Ckmeans.1d.dp, testthat, knitr, rmarkdown

Linking to BH, Rcpp

See at CRAN